document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=212135>Question 212135</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the hypotenuse of a right triangle is twice as long as one of the legs and 6 inches longer than the other. what are the lengths of the sides of the triangle </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #160213 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=160213\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The hypotenuse of a right triangle is twice as long as one of the legs and 6 inches longer than the other. what are the lengths of the sides of the triangle\r<BR>\n" );
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document.write( "Step 1.  Let x be length of one of the legs.  Then x+6 is the length of the other leg. And length of hypotenuse is 2x.\r<BR>\n" );
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document.write( "Step 2. Pythagorean Theorem.  Sum of the squares of the legs is equal to the square of the hypotenuse.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28x%2B6%29%5E2=%282x%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%2B6%29%5E2=%282x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify right side,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28x%2B6%29%5E2=4x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%2B6%29%5E2=4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract x^2 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28x%2B6%29%5E2-x%5E2=4x%5E2-x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%2B6%29%5E2-x%5E2=4x%5E2-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28x%2B6%29%5E2-x%5E2=3x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%2B6%29%5E2-x%5E2=3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify left side and multiply out the square term of x+6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B12x%2B36=3x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B12x%2B36=3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract the left side of equation on both sides by itself to get zero on the left side.  That is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B12x%2B36-%28x%5E2%2B12x%2B36%29=3x%5E2-%28x%5E2%2B12x%2B36%29 ALIGN=MIDDLE  ALT=\"x%5E2%2B12x%2B36-%28x%5E2%2B12x%2B36%29=3x%5E2-%28x%5E2%2B12x%2B36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplifying both sides of equation yields\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=2x%5E2-12x-36 ALIGN=MIDDLE  ALT=\"0=2x%5E2-12x-36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 3.  This is now a quadratic equation where we can use the quadratic formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where a=2, b=-12, c=-36\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B-12x%2B-36+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-12x%2B-36+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
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document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-12%29%5E2-4%2A2%2A-36=432 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-12%29%5E2-4%2A2%2A-36=432\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=432 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--12%2B-sqrt%28+432+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--12%2B-sqrt%28+432+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-12%29%2Bsqrt%28+432+%29%29%2F2%5C2+=+8.19615242270663 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-12%29%2Bsqrt%28+432+%29%29%2F2%5C2+=+8.19615242270663\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-12%29-sqrt%28+432+%29%29%2F2%5C2+=+-2.19615242270663 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-12%29-sqrt%28+432+%29%29%2F2%5C2+=+-2.19615242270663\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B-12x%2B-36 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-12x%2B-36\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B-12x%2B-36+=+2%28x-8.19615242270663%29%2A%28x--2.19615242270663%29 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-12x%2B-36+=+2%28x-8.19615242270663%29%2A%28x--2.19615242270663%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 8.19615242270663, -2.19615242270663.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-12%2Ax%2B-36+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-12%2Ax%2B-36+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Step 4.  Pick the positive number since we have only positive lengths.  In this case, it's 8.196. so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8.196 ALIGN=MIDDLE  ALT=\"x=8.196\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Length of one leg\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B6=14.196 ALIGN=MIDDLE  ALT=\"x%2B6=14.196\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Length of other Leg\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=28.392 ALIGN=MIDDLE  ALT=\"2x=28.392\"   DISABLED_style= \"max-width:90%; height:auto;\" >    Length of hypotenuse.\r<BR>\n" );
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document.write( "You can use the Pythagorean Theorem to check if its close to verify your answer.\r<BR>\n" );
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document.write( "For Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra.\r<BR>\n" );
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document.write( "For more info, contact Professor John Santiago at john@e-liteworks.com </SPAN>\n" );
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